Sombra, MartínReig Fité, Oriol2024-12-092024-12-092024-06-04https://hdl.handle.net/2445/216960Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Martín SombraIn this Master Final Project I have studied Berkovich spaces, which is one of the existing approaches to non-Archimedean geometry, a branch that deals with analytic spaces over non-Archimedean fields. Let us first give some context on $p$-adic geometry and the necessity to develop such a theory of analytic spaces. Any norm gives rise to a metric space by setting the distance between two elements as the norm of their difference. In the case of a metric space induced by a non-Archimedean norm, the topological space is totally disconnected. For this reason, when we try to develop a theory of analytic functions similar that for the complex case (i.e., the Archimedean case), we encounter some notorious problems.68 p.application/pdfengcc by-nc-nd (c) Oriol Reig Fité, 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/Anàlisi p-àdicaEspais topològicsTreballs de fi de màsterEspais analíticsp-adic analysisTopological spacesMaster's thesisAnalytic spacesinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess